Question 1

# How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent? 8 . 6C4 . 7C4 6 . 7 . 8C4 6 . 8 . 7C4 7 . 6C4 . 8C4

Solution

D.

7 . 6C4 . 8C4

Other than S, seven letters M, I, I, I, P, P, I can be arranged in 7!/2! 4!=7 . 5 . 3.
Now four S can be placed in 8 spaces in 8 C4 ways. Desired number of ways = 7 . 5 . 3 . 8C4 = 7 . 6C4 . 8C4.

Question 2

## How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order? 120 480 360 240

Solution

C.

360

A total number of ways in which all letters can be arranged in alphabetical order = 6! There are two vowels in the word GARDEN. A total number of ways in which these two vowels can be arranged = 2!
∴ Total number of required ways
∴ Total number of required ways

Question 3

## If m is the AMN of two distinct real numbers l and n (l,n>1) and G1, G2, and G3 are three geometric means between l and n, then  equals 4l2 mn 4lm2n 4 lmn2 4l2m2n2

Solution

B.

4lm2n

Given,
m is the AM of and n
l +n = 2m
and G1, G2, G3, n are in GP
Let r be the common ratio of this GP
G1 = lr
G2 =lr2
G3= lr3
n = lr4

Question 4

Solution

B.

192

Question 5

## The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is 5 8C3 38 21

Solution

D.

21

The required number of ways